So, the solution is to deny them immortality. Right?

I'm continually amazed by people who think that conflate the concepts of whether immortality is a sensible choice for any given individual and whether it's ok to decide, for all of humanity, whether the choice should even be available. (And, almost invariably, answer the latter question in the affirmative, and furthermore usually decide that no, the choice should not be available.)

My answer to statements, or questions, or insinuations (like the one in the parent) that maybe it's not a good idea to be immortal, is:

"By all means, don't be immortal. Go ahead and die. I won't stop you."

But don't think you have any right to make that decision for me.